Shapley Facility Location Games
Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of competition in a variety of scenarios. In a typical facility location game, users/customers/voters are mapped to a metric space representing their preferences, and each player picks a point (facility) in that space. In most facility location games considered in the literature, users are assumed to act deterministically: given the facilities chosen by the players, users are attracted to their nearest facility. This paper introduces facility location games with probabilistic attraction, dubbed Shapley facility location games, due to a surprising connection to the Shapley value. The specific attraction function we adopt in this model is aligned with the recent findings of the behavioral economics literature on choice prediction. Given this model, our first main result is that Shapley facility location games are potential games; hence, they possess pure Nash equilibrium. Moreover, the latter is true for any compact user space, any user distribution over that space, and any number of players. Note that this is in sharp contrast to Hotelling facility location games. In our second main result we show that under the assumption that players can compute an approximate best response, approximate equilibrium profiles can be learned efficiently by the players via dynamics. Our third main result is a bound on the Price of Anarchy of this class of games, as well as showing the bound is tight. Ultimately, we show that player payoffs coincide with their Shapley value in a coalition game, where coalition gains are the social welfare of the users.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 740435).
- 2.Awerbuch, B., Azar, Y., Epstein, A., Mirrokni, V.S., Skopalik, A.: Fast convergence to nearly optimal solutions in potential games. In: Proceedings of the 9th ACM Conference on Electronic Commerce, pp. 264–273. ACM (2008)Google Scholar
- 4.Ben-Basat, R., Tennenholtz, M., Kurland, O.: The probability ranking principle is not optimal in adversarial retrieval settings. In: Proceedings of the 2015 International Conference on the Theory of Information Retrieval, ICTIR 2015, Northampton, Massachusetts, USA, 27–30 September 2015, pp. 51–60 (2015)Google Scholar
- 5.Brenner, S.: Location (hotelling) games and applications. In: Wiley Encyclopedia of Operations Research and Management Science (2011)Google Scholar
- 7.Chien, S., Sinclair, A.: Convergence to approximate nash equilibria in congestion games. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 169–178. Society for Industrial and Applied Mathematics (2007)Google Scholar
- 10.Erev, I., Ert, E., Plonsky, O.: From anomalies to forecasts: a choice prediction competition for decisions under risk and ambiguity. Technical report, Mimeo, pp. 1–56 (2015)Google Scholar
- 13.Feldman, M., Fiat, A., Obraztsova, S.: Variations on the hotelling-downs model. In: Thirtieth AAAI Conference on Artificial Intelligence (2016)Google Scholar
- 15.Izsak, P., Raiber, F., Kurland, O., Tennenholtz, M.: The search duel: a response to a strong ranker. In: Proceedings of the 37th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 919–922. ACM (2014)Google Scholar
- 21.Plonsky, O., Erev, I., Hazan, T., Tennenholtz, M.: Psychological forest: Predicting human behavior (2017)Google Scholar
- 22.Procaccia, A., Tennenholtz, M.: Approximate mechanism design without money. In: EC-09 (2009)Google Scholar
- 24.Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 513–522. ACM (2009)Google Scholar
- 25.Schummer, J., Vohra, R.: Mechanism design without money. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.) Algorithmic Game Theory, pp. 110–130. Cambridge University Press (2007)Google Scholar
- 28.Shapley, L.S.: A value for n-person games. Techncial report, DTIC Document (1952)Google Scholar
- 29.Shen, W., Wang, Z.: Hotelling-downs model with limited attraction. In: Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, pp. 660–668. International Foundation for Autonomous Agents and Multiagent Systems (2017)Google Scholar